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A remainder of zero is obtained whenever the number is divided by its factor. For example, when 20 is divided by either 1,2,4,5,10 or 20 the remainder is zero. Every number has 1 as its divisor.Infact, this is the definition of divisor- a number which divides another number to return zero as the remainder.
First note that when you divide any number by the 10, the remainder will be the same number as the units digit. For example, when 26 is divided by 10, the remainder is 6 and when 37832728 is divided by 10, the remainder is 8. For this problem, we just need to know what the units digit of the number 2^400. So let's see if we can see a pattern. 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32, and 2^6 = 64. The pattern we are looking for is the value of the units digit. It is 2, 4, 8, 6, 2, 4, 8, 6, and it repeats. Every fourth remainder is 8 and since 400 is a multiple of 4, 2^400 will have 6 as its units whatever the number is and therefore the remainder will be 6. Hope that helps :)
20 if you divide by 17. 19 if you divide by 16. 18 if you divide by 15, 17 if you divide by 14. And so on. In fact any number from 10 to 99. That is, every two digit number.
Yes, it is. It can be determined in moments, without doing the division, by calculating the core digit of the number, which is 9. Every number with a core digit value of 9 is a multiple of 9, and therefore a multiple of 3.
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